“Do not come to Europe,” said Donald Tusk, the president of the European Council, which represents the bloc’s 28 leaders. “Do not believe the smugglers. Do not risk your lives and your money. It is all for nothing. Greece or any other European country will no longer be a transit country.”

Mr. Tusk’s speech at a news conference in Greece revealed just how troubled and powerless Europe has become. He beseeched people desperate for a better life to please help Europe by staying away. He once again asked Turkey, already hosting more than two million refugees from the Syria war, to please help Europe by keeping them away.

The blunt remarks came as Europe’s most recent approach to the crisis — to block passage from Greece — has left many thousands of people trapped in a nation with severe economic problems and little capacity to cope. Already nearly 10,000 are camped around Idomeni, a village on Greece’s border with Macedonia, where violent clashes have erupted. Almost every day, a new migrant camp opens.